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Math Help - Finding critical points in an equation with logarithmic expressions and exponents??

  1. #1
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    Finding critical points in an equation with logarithmic expressions and exponents??

    So I'm trying to find the minimum and maximum values of this equation, and to do that I need to find the critical point(s).

    f(x) = (x^5)(e^(6x))

    I started by taking the derivative, using the product rule...

    f'(x) = (5x^4)(e^(6x)) + (x^5)(6e^(6x))

    If I set the left side to 0 I should be able to solve for x, but I have no idea where to begin!
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  2. #2
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    Quote Originally Posted by theant4 View Post
    So I'm trying to find the minimum and maximum values of this equation, and to do that I need to find the critical point(s).

    f(x) = (x^5)(e^(6x))

    I started by taking the derivative, using the product rule...

    f'(x) = (5x^4)(e^{6x}) + (x^5)(6e^{6x})

    If I set the left side to 0 I should be able to solve for x, but I have no idea where to begin!
    Factor!

    (5x^4)(e^{6x}) + (x^5)(6e^{6x})=x^4e^{6x}(5+6x)
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